Cross Moments Research Articles

MCA: Moment Channel Attention Networks

Channel attention mechanisms endeavor to recalibrate channel weights to enhance representation abilities of networks. However, mainstream methods often rely solely on global average pooling as the feature squeezer, which significantly limits the overall potential of models. In this paper, we investigate the statistical moments of feature maps within a neural network. Our findings highlight the critical role of high-order moments in enhancing model capacity. Consequently, we introduce a flexible and comprehensive mechanism termed Extensive Moment Aggregation (EMA) to capture the global spatial context. Building upon this mechanism, we propose the Moment Channel Attention (MCA) framework, which efficiently incorporates multiple levels of moment-based information while minimizing additional computation costs through our Cross Moment Convolution (CMC) module. The CMC module via channel-wise convolution layer to capture multiple order moment information as well as cross channel features. The MCA block is designed to be lightweight and easily integrated into a variety of neural network architectures. Experimental results on classical image classification, object detection, and instance segmentation tasks demonstrate that our proposed method achieves state-of-the-art results, outperforming existing channel attention methods.

Estimating Linear Dynamic Panels with Recentered Moments

This paper proposes estimating linear dynamic panels by explicitly exploiting the endogeneity of lagged dependent variables and expressing the crossmoments between the endogenous lagged dependent variables and disturbances in terms of model parameters. These moments, when recentered, form the basis for model estimation. The resulting estimator’s asymptotic properties are derived under different asymptotic regimes (large number of cross-sectional units or long time spans), stable conditions (with or without a unit root), and error characteristics (homoskedasticity or heteroskedasticity of different forms). Monte Carlo experiments show that it has very good finite-sample performance.

Some results on quadratic credibility premium using the balanced loss function

PurposeThis paper generalizes the quadratic framework introduced by Le Courtois (2016) and Sumpf (2018), to obtain new credibility premiums in the balanced case, i.e. under the balanced squared error loss function. More precisely, the authors construct a quadratic credibility framework under the net quadratic loss function where premiums are estimated based on the values of past observations and of past squared observations under the parametric and the non-parametric approaches, this framework is useful for the practitioner who wants to explicitly take into account higher order (cross) moments of past data.Design/methodology/approachIn the actuarial field, credibility theory is an empirical model used to calculate the premium. One of the crucial tasks of the actuary in the insurance company is to design a tariff structure that will fairly distribute the burden of claims among insureds. In this work, the authors use the weighted balanced loss function (WBLF, henceforth) to obtain new credibility premiums, and WBLF is a generalized loss function introduced by Zellner (1994) (see Gupta and Berger (1994), pp. 371-390) which appears also in Dey et al. (1999) and Farsipour and Asgharzadhe (2004).FindingsThe authors declare that there is no conflict of interest and the funding information is not applicable.Research limitations/implicationsThis work is motivated by the following: quadratic credibility premium under the balanced loss function is useful for the practitioner who wants to explicitly take into account higher order (cross) moments and new effects such as the clustering effect to finding a premium more credible and more precise, which arranges both parts: the insurer and the insured. Also, it is easy to apply for parametric and non-parametric approaches. In addition, the formulas of the parametric (Poisson–gamma case) and the non-parametric approach are simple in form and may be used to find a more flexible premium in many special cases. On the other hand, this work neglects the semi-parametric approach because it is rarely used by practitioners.Practical implicationsThere are several examples of actuarial science (credibility).Originality/valueIn this paper, the authors used the WBLF and a quadratic adjustment to obtain new credibility premiums. More precisely, the authors construct a quadratic credibility framework under the net quadratic loss function where premiums are estimated based on the values of past observations and of past squared observations under the parametric and the non-parametric approaches, this framework is useful for the practitioner who wants to explicitly take into account higher order (cross) moments of past data.

Optimal area variation for maximum stiffness isostatic beams under parametric linear distributed loads

The stiffness maximization of elastic straight Euler-Bernoulli beams under the action of linearly distributed loads is addressed. The goal is achieved by minimizing the average compliance, which is given by the value of internal elastic energy distributed over the length of the beam. Studies in the literature suggest considering this approach since it provides, unlike the minimization of the maximum deflection, a constant bending stress behavior along the beam axis. An isoperimetric constraint on the material volume is also considered and optimal solutions are derived by means of calculus of variations. Three types of boundary conditions are discussed, namely cantilever, simply supported and guided-simply supported beams. Introducing a well known relation between the cross sectional area and moment of inertia, closed-form solutions for several cross sections commonly used in engineering are derived. Finally, a sensitivity analysis with respect to the load parameters is addressed within a numerical example.

Least squares moment identification of binary regression mixture models

We consider finite mixtures of generalized linear models with binary output. We prove that cross moments (between the output and the regression variables) up to order three are sufficient to identify all parameters of the model. We propose a least-squares estimation method based on those moments and we prove the consistency and the Gaussian asymptotic behavior of the estimator. We provide simulation results and comparisons with likelihood methods. Numerical experiments were conducted using the R-package morpheus that we developed for our least-squares moment method and with the R-package flexmix for likelihood methods. We then give some possible extensions to finite mixtures of regressions with binary output including both continuous and categorical covariates, and possibly longitudinal data.

A Versatile Stochastic Duel Game

This paper deals with a standard stochastic game model with a continuum of states under the duel-type setup. It newly proposes a hybrid model of game theory and the fluctuation process, which could be applied for various practical decision making situations. The unique theoretical stochastic game model is targeted to analyze a two-person duel-type game in the time domain. The parameters for strategic decisions including the moments of crossings, prior crossings, and the optimal number of iterations to get the highest winning chance are obtained by the compact closed joint functional. This paper also demonstrates the usage of a new time based stochastic game model by analyzing a conventional duel game model in the distance domain and briefly explains how to build strategies for an atypical business case to show how this theoretical model works.

Investigation of modal properties and layout of elastomer diaphragm tanks in telecommunication satellite

Elastomer diaphragm tanks have been adopted in many spacecraft applications, such as upper stages, space platforms, commercial and civil spacecraft as a propellant tank in which liquid propellant is covered with a diaphragm and compressed into a combustion chamber by gas pressure. Investigating the dynamic response and the influence of various parameters on the modal properties is a significant issue in the modeling of the space diaphragm tanks. In this work, the numerical study is presented to investigate the modal properties of a spherical fuel tank in both uncovered and covered cases with a flexible diaphragm as fluid–structure interacting situations. The filling volume ratio of fluid ranges is from 25 to 50%. Numeric dynamic simulations created by ANSYS software are verified by the experimental results of test tank and then, the validation of the numeric model is used to determine the natural frequencies and mode shapes of really elastomer diaphragm tank as the second case study for two conditions: fluid filling volume ratio of 80% that the tank is in full load condition and liquid filling volume ratio of 14% when the diaphragm completely inverted. After that, the best layout of diaphragm tanks in two-story satellite is detected by calculating deviations from center of gravity and cross moments of inertia objective functions in multi objective optimization software. Then the natural frequencies of satellite include diaphragm tanks computed and compared with natural frequencies and static loads of launch vehicle requirements. The achieved results of this study showed that the numeric simulations are able to renovate the experimental vibration characteristics of the diaphragm tank with a good precision. In addition numeric model can detect the best layout of diaphragm tank components.

Acoustic and geoacoustic inverse problems in randomly perturbed shallow-water environments.

The main goal of this paper is to estimate the regional acoustic and geoacoustic shallow-water environment from data collected by a vertical hydrophone array and transmitted by distant time-harmonic point sources. The aim is to estimate the statistical properties of the random fluctuations of the index of refraction in the water column and the characteristics of the sea bottom. It is explained from first principles how acoustic wave propagation can be expressed as Markovian dynamics for the complex mode amplitudes of the sound pressure. This makes it possible to express the cross moments of the sound pressure in terms of the parameters to be estimated. Then it is shown how the estimation problem can be formulated as a nonlinear inverse problem using this formulation, which can be solved by minimization of a misfit function. The method is applied to experimental data collected by the Acoustic Laboratory for Marine Applications system. A Bayesian analysis quantifies the uncertainty of the estimation.

A decision support system for satellite layout integrating multi-objective optimization and multi-attribute decision making

A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the C.G. offset, the cross moments of inertia and the space debris impact risk), we develop a threedimensional layout optimization model. Unlike most of the previous works just focusing on mass characteristics of the system, a space debris impact risk index is developed. Secondly, we develop an efficient optimization framework for the integration of computer-aided design (CAD) software as well as the optimization algorithm to obtain the Pareto front of the layout optimization problem. Thirdly, after obtaining the candidate solutions, we present a multi-attribute decision making approach, which integrates the smart Pareto filter and the correlation coefficient and standard deviation (CCSD) method to select the best tradeoff solutions on the optimal Pareto fronts. Finally, the framework and the decision making approach are applied to a case study of a satellite platform.

Differentially private data publishing via cross-moment microaggregation

Differential privacy is one of the most prominent privacy notions in the field of anonymization. However, its strong privacy guarantees very often come at the expense of significantly degrading the utility of the protected data. To cope with this, numerous mechanisms have been studied that reduce the sensitivity of the data and hence the noise required to satisfy this notion. In this paper, we present a generalization of classical microaggregation, where the aggregated records are replaced by the group mean and additional statistical measures, with the purpose of evaluating it as a sensitivity reduction mechanism. We propose an anonymization methodology for numerical microdata in which the target of protection is a data set microaggregated in this generalized way, and the disclosure risk limitation is guaranteed through differential privacy via record-level perturbation. Specifically, we describe three anonymization algorithms where microaggregation can be applied to either entire records or groups of attributes independently. Our theoretical analysis computes the sensitivities of the first two central cross moments; we apply fundamental results from matrix perturbation theory to derive sensitivity bounds on the eigenvalues and eigenvectors of the covariance and coskewness matrices. Our extensive experimental evaluation shows that data utility can be enhanced significantly for medium to large sizes of the microaggregation groups. For this range of group sizes, we find experimental evidence that our approach can provide not only higher utility but also higher privacy than traditional microaggregation.

A Convex Optimization Approach for Computing Correlated Choice Probabilities With Many Alternatives

A popular discrete choice model that incorporates correlation information is the multinomial probit (MNP) model where the random utilities of the alternatives are chosen from a multivariate normal distribution. Computing the choice probabilities is challenging in the MNP model when the number of alternatives is large. Mishra et al. (IEEE Transactions on Automatic Control, 2012) have proposed a semidefinite optimization approach to compute choice probabilities for the distribution of the random utilities that maximizes expected agent utility given only the mean, variance, and covariance information. Their model is referred to as the cross moment (CMM) model. Computing the choice probabilities with many alternatives is challenging in the CMM model, since one needs to solve large-scale semidefinite programs. We develop a simpler formulation as a representative agent model by maximizing over the choice probabilities in the unit simplex where the objective function is the sum of the expected utilities and a strongly concave perturbation function. By characterizing the perturbation function for the CMM model and its gradient, we develop a simple first-order gradient method with inexact line search to compute choice probabilities. We establish local linear convergence of this algorithm under mild assumptions on the choice probabilities. An implication of our results is that inverting the choice probabilities to compute the mean utilities is straightforward given any positive-definite covariance matrix. Numerical experiments show that this method can compute choice probabilities for a large number of alternatives within a reasonable amount of time while explicitly capturing the correlation information. Comparisons with simulation methods for MNP and semidefinite programming methods for CMM indicate the efficacy of the method.

The influence of shape on the vibratory response of variable beams

Pure analytical solution for variable cantilever beams subjected to free bending oscillations and inertial forces is presented in this paper. Following the Euler-Bernoulli scheme for light slender cross section beams and Henri Bouasses’s analytical procedure the in-plane linear motion differential equation is deduced. Taking into account the beam’s shape a generalized non-dimensional differential equation is derived and characterized by only four geometric parameters. Beam’s shape whose cross section area and moment of inertia variation obey a power law with respect to the longitudinal distance to the tip section of the bar and truncation are considered. The differential equation is analytically solved using the symbolic Wolfram Mathematica module for a number of typical shapes from uniform to zero area tip section with linear to cubic root variation and both rectangular and circular cross sections. The natural frequencies are determined and compared. Applications of results to high-rise building design and variable beams found in nature like tree stem are suggested.

An inequality unscented transformation for estimating the statistical moments

• A classification method for point estimate method (PEM) is suggested. • The error of Nataf transformation based PEMs is derived. • A new PEM called inequality unscented transformation (IUT) is proposed. • IUT reduces the number of sigma points compared with other high accuracy PEMs. • IUT handles correlated and asymmetric random inputs and matches cross moments. Point estimate method (PEM) is convenient for estimating statistical moments. This paper focuses on discussing the existing PEMs and presenting a new PEM for the efficient and accurate estimation of statistical moments. Firstly, a classification method of PEMs is proposed based on the strategy of choosing sigma points. Secondly, the minimum number of sigma points and the error of inverse Nataf transformation are derived corresponding to certain order and dimensionality of PEMs. Then the inequality unscented transformation (IUT) is presented to estimate the statistical moments. The proposed IUT permits the existing of limited errors in the matching of the first several order moments to decrease the number of sigma points, it opens new strategy of PEMs. The proposed method has two advantages. The first advantage is overcoming the growth of the number of sigma points with dimensionality since it parameterizes the number of sigma points and accuracy order. The second advantage is the wide applicability, for it has the ability to handle correlated and asymmetric random input variables and to match cross moments. Numerical and engineering results show the good accuracy and efficiency of the proposed IUT.

A Novel Semiparametric Hidden Markov Model for Process Failure Mode Identification

The emitting distributions of a hidden Markov model (HMM) are normally constructed using the cross moments of the process variables. Similar to the mean of a univariate probability distribution, the cross moment is the most fundamental statistic of a multivariate probability distribution, which is not capable of capturing the high-order statistical features of process data. To alleviate this limitation, the high-order equivalence of the cross moment demonstrated in this paper, as the complete dependence structure, is used to construct the emitting distribution for HMM. The complete dependence structure among the process variables is modeled in a Gaussian copula. A semiparametric data transformation is also proposed to ensure the necessary conditions for using a Gaussian copula are met. The final emitting distribution is constructed as a finite mixture of the copula models. The proposed HMM is tested on two industrial studies for performance validation. Note to Practitioners —Gaussian mixture model HMM (GMM-HMM) is an efficient and easy-to-implement tool for mode identification of dynamic industrial processes. These virtues of GMM-HMM mainly come from the use of Gaussian emitting distribution, which allows closed-form derivatives to be computed for the expectation and maximization (EM) estimation of mode parameters. The main novelty of the proposed copula mixture model HMM (SPCMM-HMM) is twofold; its emitting distribution also belongs to the exponential family, thus enabling efficient estimation of parameters through an exact EM procedure; meanwhile, it is also capable of characterizing complex dependence structures among process variables. However, the proposed SPCMM-HMM has more model parameters compared with the GMM-HMM. It excels in situations where the operation of the process system being monitored is highly integrated (with complex process variable interactions) and abundance of training data samples is available. In this paper, the interactions between process variables in both case studies are complex due to the implementation of multiple closed control loops, and a large amount of training data samples can be easily generated from simulation. The performance of the SPCMM-HMM is shown to be consistently better than that of the GMM-HMM under such settings, which are fairly common in modern industrial processes. Nonetheless, if the process system being considered is only designed for a simple operation or there is a scarcity of training data samples, the GMM-HMM is still the preferred method as it is less prone to overfitting.

Design, characterization and applications of a novel soft actuator driven by flexible shafts

This work presents a novel soft actuator with a 3D-printed elastic body based on a fused-deposition-modeling technique and with tendon actuation based on flexible shafts, which allow push, pull, and twist torque transmissions. The combination of the soft body and flexible shaft furnishes an easy-making, modular and functional unit that possesses softness and enables three degrees of freedom. We derive the kinematics and statics of the actuator based on the assumption of piecewise constant curvature, and identify the parameters experimentally. To understand the performance of the soft actuator in different design and fabrication settings, extensive experiments are performed to compare different shapes of cross sections, infill densities, infill patterns, dentation structures and moment arms in terms of generating forces under the same pulling forces. In addition, experimental validations are performed to characterize other properties such as workspace, hysteresis, pushing force, transmitted torque, and tip force under both bending and twisting. Finally, three potential applications, i.e., a soft robotic hand, a multisegment continuum robot, and a miniaturized drilling device, are prototyped and presented experimentally where the flexibility endowed by the shafts is demonstrated and highlighted. The scalability and modularity are also showcased in the three applications.

12.14: Ultimate response and design of stainless steel continuous beams

ABSTRACTDue to lack of available experimental data, plastic design of stainless steel (SS) indeterminate structures is currently not permitted by Eurocode 3: Part 1.4, despite the excellent material ductility and the existence of a Class 1 slenderness limit, thereby compromising design efficiency. The high initial material cost warrants the development of novel design procedures, in line with the observed structural response, which fully utilise its merits, improve cost‐effectiveness and minimise material consumption. This paper focuses on the response and design of stainless steel continuous beams. FE models of austenitic and lean duplex stainless steel SHS and RHS were developed and validated against published test data. The validated FE models were used to conduct parametric studies, in order to obtain structural performance data over a range of cross‐sectional slendernesses, cross section aspect ratios, moment gradients and loading arrangements. Based on obtained results, it was concluded that the current Eurocode 3: Part 1.4 approach significantly underestimates the strength of continuous beams. This is because the formation of successive plastic hinges and moment redistribution in indeterminate structures with adequate deformation capacity, as well as the effect of strain‐hardening at cross‐sectional level, are not accounted for. It is shown that accounting for both strain‐hardening and moment redistribution is of paramount importance for design. To this end, the application of the Continuous Strength Method (CSM), which rationally accounts for local buckling at cross‐section level, is extended to the design of stainless steel indeterminate structures. Further research is underway to quantify the effect of high shear stresses on the design procedure and to extend the method to the design of pinned based and fixed based stainless steel frames.

A Unified Moment-Based Approach for the Evaluation of the Outage Probability With Noise and Interference

In this paper, we develop a novel moment-based approach for the evaluation of the outage probability (OP) in a generalized fading environment with interference and noise. Our method is based on the derivation of a power series expansion of OP of the signal-to-interference-plus-noise ratio. It does not necessitate stringent requirements, the only major ones being the existence of a power series expansion of the cumulative distribution function of the desired user power and the knowledge of the cross moments of the interferers’ powers. The newly derived formula is shown to be applicable for most of the well-practical fading models of the desired user under some assumptions on the parameters of the powers’ distributions. A further advantage of our method is that it is applicable irrespective of the nature of the fading models of the interfering powers, the only requirement being the perfect knowledge of their cross moments. In order to illustrate the wide scope of applicability of our technique, we present a convergence study of the provided formula for the Generalized Gamma and the Rice fading models. Moreover, we show that our analysis has direct bearing on recent multi-channel applications using selection diversity techniques. Finally, we assess by simulations the accuracy of the proposed formula for various fading environments.

Inelastic cross sections, overlap functions and moments from ISR to LHC energies in proton interactions

We investigated the energy dependence of the parton–parton inelastic cross sections, parton–parton inelastic overlap functions and the Cq moments in proton interactions from to 14000 GeV. The approach we used is based on a phenomenological procedure where elastic and inelastic proton observables are described in a connected way by exploring the unitarity of the S-matrix. Applying a quantum-chromodynamics-inspired eikonal model, that contains contributions of the quark–quark, quark–gluon and gluon–gluon interactions, theoretical predictions on inelastic cross sections and Cq moments are compared with measurements and show a successful description of the experimental data. The Koba–Nielson–Olesen hypothesis violation is discussed as a consequence of the semihard contribution to the multiparticle production in the interactions, in accordance with several experimental and theoretical previous results. A prediction of the ratio as a function of the collision energy is presented and also compared with the experimental information.

Multiplicity counting from fission chamber signals in the current mode

In nuclear safeguards, estimation of sample parameters using neutron-based non-destructive assay methods is traditionally based on multiplicity counting with thermal neutron detectors in the pulse mode. These methods in general require multi-channel analysers and various dead time correction methods. This paper proposes and elaborates on an alternative method, which is based on fast neutron measurements with fission chambers in the current mode. A theory of “multiplicity counting” with fission chambers is developed by incorporating Böhnel's concept of superfission [1] into a master equation formalism, developed recently by the present authors for the statistical theory of fission chamber signals [2,3]. Explicit expressions are derived for the first three central auto- and cross moments (cumulants) of the signals of up to three detectors. These constitute the generalisation of the traditional Campbell relationships for the case when the incoming events represent a compound Poisson distribution. Because now the expressions contain the factorial moments of the compound source, they contain the same information as the singles, doubles and triples rates of traditional multiplicity counting. The results show that in addition to the detector efficiency, the detector pulse shape also enters the formulas; hence, the method requires a more involved calibration than the traditional method of multiplicity counting. However, the method has some advantages by not needing dead time corrections, as well as having a simpler and more efficient data processing procedure, in particular for cross-correlations between different detectors, than the traditional multiplicity counting methods.

The SEIQS stochastic epidemic model with external source of infection

This paper deals with a stochastic epidemic model for computer viruses with latent and quarantine periods, and two sources of infection: internal and external. All sojourn times are considered random variables which are assumed to be independent and exponentially distributed. For this model extinction and hazard times are analyzed, giving results for their Laplace transforms and moments. The transient behavior is considered by studying the number of times that computers are susceptible, exposed, infectious and quarantined during a period of time (0, t] and results for their joint and marginal distributions, moments and cross moments are presented. In order to give light this analysis, some numerical examples are showed.